(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known dataA lunar probe is given just escape speed at an altitude of .25 DU and flight path angle 30°. How long will it take the probe to get to the vicinity of the moon (r = 60 DU), disregarding the moon's gravity?

Circular orbit, radius = 1.25 DU

θ = 30°

gravitational parameter = μ = 1 DU^3/TU^2

true anomaly = v

Eccentric Anomaly = E

eccentricity = e

t-to = Time of flight

a = semi-major axis

2. Relevant equationsEscape velocity = √(2μ/r) = 1.26 DU/TU

tan(θ) = (esin v)/(1 + ecos v)

tan (v/2) = √((1+e)/(1-e))tan(E/2)

t-to = √(a^3/μ)(2k(pi) + (E-esinE) - (Eo - esinEo))

θ(parabolic) = v/2

3. The attempt at a solution

The answer is 223.2TU

I just can't see how flight path relates to time of flight. The second equation in the relevant equations section seems like it would fit for equating flight path and true anomaly but I can't separate the true anomaly variable. I'm not sure if that last equation for a parabolic flight path applies (the orbit is parabolic but I don't know). Any help would be greatly appreciated.

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# Time of Flight using flight path and radius (Kepler's Equation)

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